Electromagnetic Waves — Questions & Answers

Sample questions from Electromagnetic Waves

1. Q1. At a certain point in space, the electric field of a plane electromagnetic wave travelling in vacuum is momentarily zero. At that instant, the total electromagnetic energy density at that point is:

   • A.Maximum, because all the energy is in the magnetic field
   • B.Half the maximum value
   • C.Zero✓
   • D.Equal to ε0 E0^2/2
   Solution

   In a plane wave E and B oscillate in phase: B = E/c at every instant. When E = 0, B = 0 also, so both ε0 E^2/2 and B^2/(2μ0) vanish and the instantaneous energy density is zero. Energy is not exchanged between E and B (unlike an LC circuit); it moves along with the wave.

2. Q2. A monochromatic plane wave falls on a blackened plate. The plate is then replaced by a mirror of the same area, and the beam intensity is halved. Compared with the original situation, the force on the plate becomes:

   • A.Half
   • B.Double
   • C.Unchanged✓
   • D.One quarter
   Solution

   Absorber force = I A/c. Reflector force = 2 I' A/c with I' = I/2, which is again I A/c. The doubling from reflection exactly compensates the halving of intensity.

3. Q3. A photon of visible light at the violet end (400 nm) and one at the red end (700 nm) are compared. The ratio of their energies, violet to red, is closest to:

   • A.0.57
   • B.3.06
   • C.1.00
   • D.1.75✓
   Solution

   E is proportional to 1/lambda, so the ratio is 700/400 = 1.75. Numerically the violet photon has 3.11 eV and the red 1.78 eV, whose ratio is 1.75.

4. Q4. The dimensional formula of the Poynting vector S = (E × B)/μ0 is:

   • A.[M L^2 T^-3]
   • B.[M T^-3]✓
   • C.[M L^-1 T^-2]
   • D.[M L T^-3]
   Solution

   The Poynting vector is power per unit area (W/m^2). Power has dimensions [M L^2 T^-3]; dividing by area [L^2] gives [M T^-3].

5. Q5. A tiny perfectly absorbing dust grain in space is pushed outward by sunlight and pulled inward by the Sun's gravity. Because both the radiation force and the gravitational force fall as 1/r^2, the net outcome for a given grain is:

   • A.Dependent on distance, with radiation winning only very close to the Sun
   • B.Independent of its distance from the Sun; a grain that is pushed out at one distance is pushed out everywhere✓
   • C.Dependent on distance, with radiation winning only very far from the Sun
   • D.Always inward, since gravity is a stronger force
   Solution

   Radiation force is (I A/c) and I falls as 1/r^2; gravity also falls as 1/r^2. Their ratio is therefore the same at every distance, fixed only by the grain's area-to-mass ratio. Small grains (large area per unit mass) are expelled at all distances, larger ones never.

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